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Possible coefficients for a given discriminant

asked 2014-11-16 22:10:59 -0600

I'm a new user of Sage, and want to know what commands should I use to determine the possible positive definite binary quadratic forms for a given discriminant? i.e the coefficients

For example if I have -47 as a discriminant for a quadratic form, and set [a,b,c]=ax^2+bxy+cy^2, then I will have :

Ro=[1,1,12] , R1=[2,1,6], R2=[3,1,4] , R4=[3,-1,4] , R4=[2,-1,6]

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answered 2014-11-19 04:26:43 -0600

Francis Clarke gravatar image

You can do:

sage: BinaryQF_reduced_representatives(-47)
[x^2 + x*y + 12*y^2,
2*x^2 - x*y + 6*y^2,
2*x^2 + x*y + 6*y^2,
3*x^2 - x*y + 4*y^2,
3*x^2 + x*y + 4*y^2]

and to get the coefficients:

sage: [qf.polynomial().coefficients() for qf in BinaryQF_reduced_representatives(-47)]
[[1, 1, 12], [2, -1, 6], [2, 1, 6], [3, -1, 4], [3, 1, 4]]
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Asked: 2014-11-16 22:10:59 -0600

Seen: 59 times

Last updated: Nov 19 '14